My thoughts on education and life in general

Double Negatives

Today, we’ll analyze the validity of this statement (made by Person X):

Going against my opinion is not an insult. If it was, I would simply delete your comment since this is my blog.

In response, another person (Person Y) said this:

Since you did not delete my comments as I quote you “If it was” then it means “It was not”. You refer to the previous statement “Going against my opinion is not an insult”. Removing the two negatives, one from each, it then becomes “Going against my opinion is an insult”. Ochams razor? Logical? I even think it is Math. Oops. It may now compel you to delete my comments. Sorry again but delete me if you must.

Let’s start with the statements made by Person X. Let

A = “Going against my opinion is an insult.”
B = “I would simply delete your comment since this is my blog.”

So writing the first quote in logical form, this corresponds to:

not A.
if A, then B.

Not we’ll go to what Person Y said. Since B did not happen, i.e., “not B”, we then conclude “not A”. We can therefore replace “if A, then B” by “not A”. We can rewrite our argument in this manner:

not A. not A.

Now if we do what was said in the second quote, “Removing the two negatives, one from each,” we will get:

A. A.

Hence the conclusion of the Person Y, “Going against my opinion is an insult.”

Logical? I think NOT. Unless repeating your argument negates your original argument. @_@ As far as I know, you can only remove two negatives if it is in this form:

not (not A) = A.

This is tantamount to saying, “It is not true that going against my opinion is not an insult.”

Of course, my assumption is that we are using logic. If Person Y is working on an entirely different mathematics using another set of axioms, I cannot argue with that. 😀